The Shrimpers' next match is against Parkinson's Bradford side on Friday, by which time they will have a new manager at the helm.
But Sturrock will be back in charge for one last match when Southend face Crewe in the Johnstone's Paint Trophy final at Wembley next month.
"Paul Sturrock is an outstanding manager," Parkinson said.
"If you look at his record it stands up against any other manager in terms of promotions.
"What the reasons for him leaving are we are not quite sure. Apparently he is going to lead the team out at Wembley which is great for him.
"But he'll have one eye on his next job and I don't think it will be too long before he is back in one."